Math Is Fun Forum

Hi,
int number 123456;
int firstDigit;
int totalDigits = (int) Math.log10(number);
firstDigit = (int) (number/ (int) Math.pow(10,totalDigits));
System.out.println("First Digit is: " + firstDigit);

how could log10 of a number like 123456 is 5?
I type that in google and it's 5.09151220163 not 5, I know we used casting so it discard the fractional parts to get 5, but my question is not about the Java it's about log10 why log10 always get the total digits with fractional parts always!
like log10 of 532 is 2.7259116323 which is 2 digits that is working! but how mathematically is that

how can Math.log10(12345) calculate the number of digits which is 5 correct!?
only that first part of the code is really ambiguous

Hi, I have this problem the solution it needs is not advanced not using "if and else statement" the book needs to see the answer with simple algebra.
I have the question and the solution but it's not understandable completely expect I know that we need mod 2 (ODD and even) in my solution.

A robot needs to tile a floor with alternating black and white tiles. Develop
an algorithm that yields the color (0 for black, 1 for white), given the row and
column number. Start with specific values for the row and column, and then
generalize

////// solution of the book start
Solution of the book :

Clearly, the answer depends only on whether
the row and column numbers are even or odd,
so let’s first take the remainder after dividing by 2. Then we can enumerate all expected
answers:

In the first three entries of the table, the color
is simply the sum of the remainders. In the
fourth entry, the sum would be 2, but we want
a zero. We can achieve that by taking another
remainder operation:
color = ( (row % 2) + (column % 2) ) % 2

////// solution of the book Ended

pls explain the book solution only I want to understand it step by step I didn't understand what he mean by dividing
note that the dividing here is integer division ex : 3/2 = 1 not 1.5 because it discard the fractional part

I didn't understand the solution from beginning like " first take the remainder after dividding by 2"
which reminder? and what number we are dividing it by 2 ?
the solution is confusing be and ambiguous

how cold write

Hi, I found this question it's very strange in math the function can be linear and exponential in such a form

this is very strange is this only happen in population problems? is anyone has a comment in this phenomenon

hi, why 1 - 1.928749848×10^(-22) equal = 1 in online calculators?
I used also google calculator :-
I tried to remove the 1 integer to become 0.928749848×10^(-22)
but still the same the sum equal 1! is there something wrong?

...
...

if f(1) = 250*a = 150
f(4) = 250* a^2 = 90

solving the equation to find a

I found similar question on a book I study from an example above in the picture :

but I made my own example with simple number to make it easy to illustrate

my problem and my question is how cold he dividing the two equations ( in my example and in the book example)
what thing gives to him the mechanism to do that to find the missing "a"
I mean they are two separate equation and lets say the f(1) is mean the time in first hour, and f(4) is the time of fourth hour
so they are different so what rules he lean on it to do such thing to solve this equation by dividing the two of them by themselves

note that I create my example from the book source itself (the answer is 0.59999 which men 60% percent I know the answer for the example I made but the answer is coming out like a magic I want to understand the concept of dividing two equations togather) :

Hello,

when I search in my " all posts " history like this :

it show me this :

it's numbered by (page 1,page 2... etc)
can you add there additional option to view all the pages at once! to make search on posts easier and more functionality